An Approximate Probabilistic Model for Structured Gaussian Elimination

Many of the fast methods for factoring integers and computing discrete logarithms require the solution of large sparse linear systems of equations over finite fields. Structured Gaussian elimination has been proposed as a first step in solving such sparse systems. It is a method for selecting pivots in an attempt to preserve the sparseness of the coefficient matrix. Eventually it terminates with a (smaller) residual linear system which must be solved by some other method. In many cases, the original column density is roughly proportional to the reciprocal of the of the column index. We discuss the asymptotic behavior of structured Gaussian elimination for this situation. One result is the observation that, for the column density just mentioned, the size of the residual system grows linearly with the size of the problem. This makes it possible to extrapolate the results of Monte Carlo simulation to much larger problems.     

ChemInform Abstract: Crystal Structures of New Alkali Metal-Rich Oxometallates: Rubidium Aluminate Tetrahydroxide,Rb9(AlO4)(OH)4, Rubidium Orthogallate,Rb5GaO4, Cesium bis-Chromate(IV) Oxide,Cs10(CrO4)2O,and Cesium Diindate,Cs8In2O7.

The crystal structures of several new alkali metal oxometallates are determined by single crystal XRD.     

Application of electric fields in NMR

Anisotropic orientation states in materials such as liquid crystals, liquid crystalline polymers or polymeric electrets can be induced by the application of electric fields. This behaviour is exploited extensively in displays or sensors. Anisotropic optical properties induced by relatively high electric field strengths are used in the well known displays made from liquid crystalline materials. The anisotropy of electric properties in polymeric materials gives rise to properties such as the high piezoelectricity of fluorine containing electrets. Attempts have been made to investigate the orientational state induced by electric fields after poling using NMR techniques. However, there is only access to the irreversible part of the electrically induced orientation. In-situ application of (high) voltages during NMR experiments enables the investigation of the influence of the electric field on molecular orientational states or electrically-induced morphological changes. The NMR methods have been modified to investigate the dynamics of reorientation processes in electric fields and to extend the possible time range towards below1ms. The application of high voltages in NMR experiments requires experimental specifications. Some of our experiences are outlined in this paper.     

Heats of formation of organic molecules by ab initio methods: Thiaalkanes

The bond energy scheme for calculating heats of formation of organic molecules from ab initio data (6–31G*) has been extended to include 24 compounds containing sulfur in the sulfide oxidation state. The rms deviation from the experimental values for these compounds is 0.54 kcal/mol, which is approximately experimental error.     

Dihydroazulene-Boron Subphthalocyanine Conjugates with Oligo(phenyleneethynylene) Bridging Unit: Photoswitchable Fluorophores

In this work, we have linked the dihydroazulene (DHA)/vinylheptafulvene (VHF) photo-/thermoswitch and the boron subphthalocyanine (BsubPc) fluorophore via an axial oligo(phenyleneethynylene) bridging unit into new DHA-BsubPc conjugates. The objectives were to elucidate the influence of BsubPc on the DHA/VHF switching reactions and the influence of DHA/VHF on the BsubPc fluorescence in these conjugates for which the entire axial substituent connected to boron comprises one large, conjugated scaffold. We present the synthesis and properties of DHA-BsubPc conjugates with varying peripheral substituents on the BsubPc core, being either unsubstituted (H₁₂BsubPc) or partially fluorinated (F₆BsubPc). Fluorination of the BsubPc core provided a remarkable increase in the reversibility of the DHA-VHF interconversions promoted by light and heat, respectively, and accompanied by on/off switching of the BsubPc fluorescence. Synthetically, the units were connected using Sonogashira coupling reactions of suitable acetylenic building blocks.     

Metal complexes with polymeric ligands: modular synthesis of multifunctional materials for applications in biomedicine and nanotechnology

Polymeric metal complexes exhibiting useful properties were prepared by chelating macroligands to labile and inert metal ions. The specific structures elucidated through this method, as well as potential applications for these complexes are described. By carefully selecting the appropriate metal ion and polymer, these materials can be tuned for a host of applications in fields ranging from biomedicine to nanotechnology.